Right I got some info in front of me and I'm going to try and work out the ev of pushing against several ranges. For my own interest if nothing else. Given the 3 bet on the turn I will assume a push will be called by any hand in villain's range.

First up BeeJall's pessimistic range:

22, 33, 55, A2s

The push will be called so the pot is effectively $66 with hero betting $36 to win it. Rather then calculating the amount won and the amount lost I will simplify the calculation and consider the ev with hero's bet added to the pot and say the amount lost when beaten is 0. This removes all terms with losing situations as multiplying by zero gives zero. So the pot is $102

HAND............Combinations..........%(win)
22....................... 1 ....................... 0/44 (no cards can come to save us)
33....................... 3 ....................... 0/44
55....................... 3 ....................... 0/44
A2s..................... 3 ....................... 32/44 (9 cards beat us)
but with A2 there are ties possible the %(tie) is 3/44

So we have 10 combinations of hands and we can ignore all but A2 as they are returning zero.

(3/10)(32/44)($102)+(3/10)(3/44)($51) = $23 We had to bet $36 so our ev against this range is $-13
Anyone want to disagree? Please feel free to point out mistakes.

So what about a more favourable range? I'll add AA and A4. I struggle to see any draws that would play like this so I'll ignore 45 or 46.

HAND............Combinations..........%(win)...... ..%(tie)
22....................... 1 ....................... 0/44 ........ 0/44
33....................... 3 ....................... 0/44 ........ 0/44
55....................... 3 ....................... 0/44 ........ 0/44
AA...................... 3 ....................... 38/44 ...... 3/44
A2s..................... 3 ....................... 32/44 ...... 3/44
A4...................... 9 ....................... 0/44 ........ 44/44

So (3/22)(38/44)($102)+(3/22)(3/44)($51)+(3/22)(32/44)($102)+(3/22)(3/44)($51)+(9/22)(44/44)($51) = $44. Subtract our bet and the EV is $8

So adding AA adds about $10 to our EV whilst A4 increases it by about $20! Add more overpairs to villain and EV rises accordingly. Well I found that useful and interesting to do, sorry if I've bored you senseless. Anyone see mistakes please point them out.